Question

jules owns a square plot of land that measures 30 yards on each side. he plans to divide the land in half by building a fence, as shown by the dotted line below. how many yards of fencing will jules need?
15 yd
30 yd
$30\sqrt{2}$ yd
$30\sqrt{3}$ yd

Explanation:

Step1: Identify the shape and formula

The plot is a square, and the fence is the diagonal of the square. For a square with side length \( s \), the length of the diagonal \( d \) is given by the Pythagorean theorem, since the diagonal forms a right triangle with two sides of the square. The Pythagorean theorem states \( d = \sqrt{s^2 + s^2} \).

Step2: Substitute the side length

Here, the side length \( s = 30 \) yards. Substituting into the formula: \( d=\sqrt{30^2 + 30^2}=\sqrt{900 + 900}=\sqrt{1800} \). Simplify \( \sqrt{1800} \): \( \sqrt{900\times2}=\sqrt{900}\times\sqrt{2}=30\sqrt{2} \).

Answer:

\( 30\sqrt{2} \) yd (corresponding to the option \( 30\sqrt{2} \) yd)